In the universities, students are generally taught problem solving through various methods and apparatus. The most obvious is the lecture and text book method. A student is assigned to read a chapter and asked to solve problems at the end of the chapter. After reading the chapter, many students will look back through the chapter for various formulae and attempt to apply those formulae to word problems.
In conjunction with this, a teacher will also give a lecture on the subject in which the student may take notes, including various formulae, and also use the notes to help solve the word problems. Thus, a particular subject should now contain one set of formulae in the text book and another set in the students notebook, preferably the same set as in the text book.
Usually teachers do not have enough time in class to show more examples and students do not have enough time to practice more examples at home. There is also a problem of remembering what was said so that the classroom notes often don't make sense to many students. Further, the student will not actually touch the formulae. He or she will have seen and written the formulae, but will have not actually touched or otherwise manipulated the formula.
In terms of sense of touch, muscle memory and hand-brain coordination are an integral component of sports training, which is traced back to human beings learning abilities developed over millions of years of evolution. As Confucius once prophesied:
“I hear and I forget
I see and I remember
I do and I understand.”
Another problem with the traditional teaching method is that a calculator is still required to solve the problems which is time consuming and requires extra equipment. Many students have problems starting and setting up word problems for several reasons. First, they often have a hard time deciding which formulae to choose. Also, they have a hard time reading which results in not quite understanding the book and how to use the formulae.
Yet still a problem arises because many students do not understand how to enter data into a calculator for a particular complex formula. Even when such calculation are performed through a calculator there is much writing and manipulating which results in a majority of time being wasted performing calculations.
By way of example, time value of money is one of the most important concepts in finance. It is usually discussed briefly in the prerequisite course for an introductory corporate finance course such as Financial Accounting or Managerial Accounting. It is more formally treated at the early chapters in Introduction to Corporate Finance and subsequently used heavily in bond and stock valuations, capital budgeting such as calculating Net Present Value of investment projects in the later chapters.
Students often have extreme difficulty with cash flow patterns such as annuities, lump sum, perpetuity and dividend constant-growth cash flow patterns, such as in determining stock valuations.
In these subject matters, students commonly make two mistakes. First, many students do not understand exactly where the present value obtained from the formulas or calculator occurs on a time line, then often conclude that the present value is the value today, but it is often the value at some time in the future or in the past. Thus, once they determine the dollar amount from the present value calculation formula, no matter in what years the cash flows occur, they simply put that amount on year zero without further discounting it to the present.
The second mistake which is more common than the first mistake, is that while some students understand that the future cash flows need to be discounted to get the present value, they do not know the correct time periods used for discounting. For example, if the first payment of an annuity is made in year ten then some students mistakenly conclude that the present value will be also at year ten instead of at year nine.
These two common mistakes are typically the result of not performing enough practice problems.